Chapter 8: Mechanical Failure

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Chapter 8 - 1

ISSUES TO ADDRESS...

• How do cracks that lead to failure form?

• How is fracture resistance quantified? How do the fracture

resistances of the different material classes compare?

• How do we estimate the stress to fracture?

• How do loading rate, loading history, and temperature

affect the failure behavior of materials?

Ship-cyclic loading

from waves.

Computer chip-cyclic

thermal loading.

Hip implant-cyclic

loading from walking.

Adapted from Fig. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.)

Adapted from Fig. 22.26(b), Callister 7e.

Chapter 8: Mechanical Failure

Adapted from chapter-opening photograph, Chapter 8, Callister & Rethwisch 8e. (by Neil Boenzi, The New York Times.)

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Chapter 8 - 2

Fracture mechanisms

• Ductile fracture

– Accompanied by significant plastic

deformation

• Brittle fracture

– Little or no plastic deformation

– Catastrophic

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Chapter 8 - 3

Ductile vs Brittle Failure

Very

Ductile

Moderately

Ductile

Brittle

Fracture

behavior:

Large

Moderate

%AR or %EL

Small

• Ductile fracture is

usually more desirable

than brittle fracture!

Adapted from Fig. 8.1, Callister & Rethwisch 8e.

• Classification:

Ductile:

Warning before

fracture

Brittle:

No

warning

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Chapter 8 - 4

• Ductile

failure:

-- one piece

-- large deformation

Figures from V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.1(a) and (b), p. 66 John Wiley and Sons, Inc., 1987. Used with permission.

Example: Pipe Failures

• Brittle

failure:

-- many pieces

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Chapter 8 - 5

• Resulting

fracture

surfaces

(steel)

50 mm

particles

serve as void

nucleation

sites.

50 mm

From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 11.28, p. 294, John Wiley and Sons, Inc., 1987. (Orig. source: P. Thornton, J. Mater. Sci., Vol. 6, 1971, pp. 347-56.)

100 mm

Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

Moderately Ductile Failure

• Failure Stages:

necking

void

nucleation

void growth

and coalescence

shearing

at surface

fracture

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Chapter 8 - 6

Moderately Ductile vs. Brittle Failure

Adapted from Fig. 8.3, Callister & Rethwisch 8e.

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Chapter 8 - 7

Brittle Failure

Arrows indicate point at which failure originated

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Chapter 8 - 8

• Inter

granular

(

between

grains)

304 S. Steel

(metal)

Polypropylene

(polymer)

Reprinted w/ permission from R.W. Hertzberg, "Defor-mation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.35(d), p. 303, John Wiley and Sons, Inc., 1996.

4 mm

• Trans

granular

(

through

grains)

Al Oxide

(ceramic)

316 S. Steel

(metal)

3 mm

160 mm

1 mm

(Orig. source: K. Friedrick, Fracture 1977, Vol. 3, ICF4, Waterloo, CA, 1977, p. 1119.)

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Chapter 8 - 9

• Stress-strain behavior (Room T):

Ideal vs Real Materials

TS << TS

_engineering

materials

perfect

materials

E/10

E/100

0.1 perfect mat’l-no flaws

carefully produced glass fiber

typical ceramic

_{typical strengthened metal}

typical polymer

• DaVinci (500 yrs ago!) observed...

-- the longer the wire, the

smaller the load for failure.

• Reasons:

-- flaws cause premature failure.

-- larger samples contain longer flaws!

Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.4. John Wiley and Sons, Inc., 1996.

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Chapter 8 - 10

Flaws are Stress Concentrators!

• Griffith Crack

where

t

= radius of curvature

o

= applied stress

m

= stress at crack tip

a

= lenght of crack

K

_t

= Stress concentration factor

(

_m

/

_o

)

t

Adapted from Fig. 8.8(a), Callister & Rethwisch 8e.

o

t

o

m

K

2 /

1

2 a

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Chapter 8 - 11

Concentration of Stress at Crack Tip

Adapted from Fig. 8.8(b), Callister & Rethwisch 8e.

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Chapter 8 - 12

Crack Creation & Propagation

Cracks having sharp tips propagate

easier than cracks having blunt tips

deformed

region

brittle

Energy balance on the crack

• Elastic strain energy-

• energy stored in material as it is elastically deformed

• this energy is released when the crack propagates

• creation of new surfaces requires energy

ductile

• Avoid sharp corners!

r ,

fillet

radius

w

h

max

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Chapter 8 - 13

Criterion for Crack Propagation

Crack propagates if crack-tip stress (

_m

)

exceeds a

critical stress

(

_c

)

where

– E = modulus of elasticity

–

_s

= specific surface energy

– a = one half length of internal crack

For ductile materials => replace

_s

with

_s

+

_p

where

_p

is plastic deformation energy

2 /

1

2 a

s

c

E

i.e.,

_m

>

_c

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Chapter 8 - 14

• Crack growth condition:

• Largest

, most highly

stressed

cracks grow first!

Design Against Crack Growth

K

Ic

=

Y

a

--Scenario 1:

Max. flaw

size dictates design stress.

max

a

Y

K

_Ic

design

a

_max

no

fracture

--Scenario 2:

Design stress

dictates max. flaw size.

2 max

1 design

Ic

Y

K

a

_max

no

fracture

K

c

= Fracture toughness

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Chapter 8 - 15

Design Example: Aircraft Wing

Answer:

(

_c

)

_B

168 MPa

• Two designs to consider...

Design A

--largest flaw is 9 mm

--failure stress = 112 MPa

Design B

--use same material

--largest flaw is 4 mm

--failure stress = ?

• Key point: Y and K

_Ic

are the same for both designs.

• Material has K

_Ic

= 26 MPa-m

0.5 • Use...

max

a

Y

K

_Ic

c

B

max

A

max

a

_c

c

9 mm

112 MPa

_{4 mm}

--Result:

=

a

=

Y

K

_Ic

constant

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Chapter 8 - 16

Impact Testing

final height

initial height

• Impact loading:

-- severe testing case

-- makes material more brittle

-- decreases toughness

Adapted from Fig. 8.12(b), Callister & Rethwisch 8e. (Fig. 8.12(b) is adapted from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and

Properties of Materials, Vol. III, Mechanical Behavior, John Wiley and Sons, Inc. (1965) p. 13.)

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Chapter 8 - 17

Influence of Temperature on

Impact Energy

• Ductile-to-Brittle Transition Temperature (DBTT)

...

BCC metals (e.g., iron at T < 914ºC)

Im

pac

t

Energy

Temperature

High strength materials (

_y

> E/150)

polymers

More Ductile

Brittle

Ductile-to-brittle

transition temperature

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Chapter 8 - 18

• Pre-WWII: The Titanic

• WWII: Liberty ships

• Problem: Steels were used having DBTT’s just below

room temperature

.

Reprinted w/ permission from R.W. Hertzberg,

"Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard, The Discovery of the Titanic.)

Reprinted w/ permission from R.W. Hertzberg,

"Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Earl R. Parker,

"Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.)

Design Strategy:

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Chapter 8 - 19

Fatigue

Adapted from Fig. 8.18, Callister & Rethwisch 8e. (Fig. 8.18 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.)

• Fatigue

= failure under applied cyclic stress.

• Stress varies with time.

-- key parameters are

S

,

_m

, and

cycling frequency

max

min

time

m

S

• Key points: Fatigue...

--can cause part failure, even though

_max

<

_y

.

--responsible for ~ 90% of mechanical engineering failures.

tension on bottom

compression on top

counter

motor

flex coupling

specimen

bearing

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Chapter 8 - 20 Adapted from Fig. 8.19(a), Callister & Rethwisch 8e.

Types of Fatigue Behavior

• Fatigue limit

,

S

_fat

:

--no fatigue if S < S

_fat

S

_fat

case for

steel

(typ.)

N = Cycles to failure

10

3

10

5

10

7

10

9 unsafe

safe

S

=

s

tress

ampl

itude

• For some materials,

there is no fatigue

limit!

Adapted from Fig. 8.19(b), Callister & Rethwisch 8e.

case for

Al

(typ.)

N = Cycles to failure

10

3

10

5

10

7

10

9 unsafe

safe

S

=

s

tress

ampl

itude

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Chapter 8 - 21

• Crack grows incrementally

typ. 1 to 6

a

~

increase in crack length per loading cycle

• Failed rotating shaft

-- crack grew even though

K

max

< K

c

-- crack grows faster as

• increases

• crack gets longer

• loading freq. increases.

crack origin

Adapted from

Fig. 8.21, Callister & Rethwisch 8e. (Fig. 8.21 is from D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.)

Rate of Fatigue Crack Growth

m

K

dN

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Chapter 8 - 22

Improving Fatigue Life

2. Remove stress

concentrators.

_{Adapted from}

Fig. 8.25, Callister & Rethwisch 8e.

bad

better

Adapted from

1. Impose compressive

surface stresses

(to suppress surface

cracks from growing)

N = Cycles to failure

moderate tensile

_m

Larger tensile

_m

S

=

s

tre

s

ampli

tude

near zero or compressive

_m

--Method 1: shot peening

put

surface

into

compression

shot

--Method 2: carburizing

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Chapter 8 - 23

Creep

Sample deformation at a constant stress ( ) vs. time

Adapted from

Primary Creep: slope (creep rate)

decreases with time.

Secondary Creep

: steady-state

i.e., constant slope

/ t)

Tertiary Creep: slope (creep rate)

increases with time, i.e. acceleration of rate.

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Chapter 8 - 24

• Occurs at elevated temperature, T > 0.4 T

_m

(in K)

Creep: Temperature Dependence

elastic

primary

secondary

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Chapter 8 - 25

Secondary Creep

• Strain rate is constant at a given T,

-- strain hardening is balanced by recovery

stress exponent (material parameter)

strain rate

activation energy for creep

(material parameter)

applied stress

material const.

• Strain rate

increases

with increasing

T,

10

2

0

4

0

10

0

2

0

10 -2

10 -1

1 Steady state creep rate (%/1000hr)

_s

St

re

ss

(MPa)

427ºC

538ºC

649ºC

Adapted from

Fig. 8.31, Callister 7e. (Fig. 8.31 is from Metals Handbook: Properties and Selection:

Stainless Steels, Tool Materials, and Special Purpose Metals, Vol. 3, 9th ed., D. Benjamin (Senior Ed.), American Society for Metals, 1980, p. 131.)

RT

Q

K

n

c

s

2 exp



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Chapter 8 -

Creep Failure

• Failure:

along grain boundaries.

applied

stress

g.b. cavities

From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.32, p. 87, John Wiley and Sons, Inc., 1987. (Orig. source: Pergamon Press, Inc.)